TOC problem in Word 2013

I have a two-page Table of Contents in a brief. Court rules require certain static text (that does not change and does not reference a page number) be interspersed between the TOC elements (lines) that carry page numbers. I paste the static text between the TOC elements, and two things happen: (1) the static text takes on the same shaded appearance on the screen as the elements (even though the static text has the "Normal" style, and (2) when I refresh the TOC, the static text disappears!

Because a Table of Contents is a reference field, anything you insert into it will be deleted next time it updates. If you want your 'static' text to appear in the Table of Contents, you need to add it to the headings that the Table of Contents references. There really is no way around this.

As Paul says, you will need to include the static text in the document proper and include that style/outline level when specifying the TOC entries.

You can tell the TOC not to include a page number for specific TOC levels. For instance the following TOC field won't show the page numbers for the outline level 1 (Heading 1) styles.
{ TOC \o "1-4" \n "1-1"}

The static text exists elsewhere in the document; I understand it's simply a matter of assigning a distinct style to the static text, which will cause the TOC to pull it into the TOC.

You also need to tell the TOC (field) to pull in that Style and what to do with it when it does (i.e. no page number, & format). This is done by modifying the field's switches and by setting the format for TOC styles (the styles for text generated by the TOC, not those which trigger inclusion in the TOC).

Yes, it is a matter of assigning a distinct style to that static text and then telling the TOC to include it without page numbers. I would recommend you edit the TOC field directly. eg The following TOC would build using the usual outline levels 1-4 and a style called 'Static' which would appear as a TOC 5 style which would not have a page number.
{ TOC \o "1-4" \t "Static,5" \n "5-5"}

You could then edit the TOC 5 style to have the appearance you wanted for these entries.